Meantone intervals

This table shows all the simple intervals of septimal meantone, which includes the entire 7-limit tonality diamond. Other relevant tables of meantone intervals are the table of quarter-comma meantone intervals and the table of 31 edo intervals.

In 12edo the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.

In 19edo, in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.

More complex meantone edos such as 31edo distinguish all intervals listed on this table.

See also Wikipedia's list of meantone intervals

Name	Size*	Ratios
Unisons
Perfect unison (P1)	0	1/1
Augmented unison (A1)	75.5	28/27~25/24~21/20
Seconds
Diminished second (d2)	42.0	128/125~64/63~50/49~36/35
Minor second (m2)	117.5	16/15~15/14
Major second (M2)	193.0	10/9~9/8
Augmented second (A2)	268.5	7/6
Thirds
Diminished third (d3)	235.0	8/7
Minor third (m3)	310.5	6/5
Major third (M3)	386.0	5/4
Augmented third (A3)	461.5	21/16
Fourths
Diminished fourth (d4)	428.0	9/7 (a bit 14/11-ish)
Perfect fourth (P4)	503.5	4/3
Augmented fourth (A4)	579.0	7/5
Double augmented fourth (AA4)	654.5	Close to 16/11
Fifths
Double diminished fifth (dd5)	545.5	Close to 11/8
Diminished fifth (d5)	621.0	10/7
Perfect fifth (P5)	696.5	3/2
Augmented fifth (A5)	772.0	14/9 (a bit 11/7-ish)
Sixths
Diminished sixth (d6)	738.5	32/21
Minor sixth (m6)	814.0	8/5
Major sixth (M6)	889.5	5/3
Augmented sixth (A6)	965.0	7/4
Sevenths
Diminished seventh (d7)	931.5	12/7
Minor seventh (m7)	1007.0	16/9~9/5
Major seventh (M7)	1082.5	15/8
Augmented seventh (A7)	1158.0	35/18~49/25~63/32
Octaves
Diminished octave (d8)	1124.5	27/14~48/25~40/21
Perfect octave (P8)	1200	2/1
Augmented octave (A8)	1275.5	25/12~21/10

* In POTE septimal meantone